Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 11-5
		
Example 1	Surface Area of a Pyramid
Find the surface area of the square pyramid.

First find the lateral area.  The lateral area of the pyramid is made up of four triangles. 

Estimate   L = 4()(3)(4) = 24 
   L	= 4 ()bh		Area of 4 triangles
	= 4 ()(3)(4.2)	Replace b with 3 and h with 4.2.
	= 25.2 ft^2		Simplify.
Then find the surface area.  The base of the pyramid is a square.
Estimate  S = 25 + 9 or 34
   S	= L + B		Write the formula
	= L + s^2		The area of a square is s^2.
	= 25.2 + 3^2		Substitution.
	= 34.2 ft^2		Simplify.  Is your answer reasonable?	

Example 2	Use Surface Area to Solve a Problem
PAINTING	A pyramid having a square base measuring 12 meters and a slant height of 18 meters needs to be painted. The pyramid sits on the ground so the bottom does not require paint. Find the surface area needing paint.

Find the lateral area only, since the bottom of the pyramid does not need painting.
Estimate  L = 4()(10)(20) = 400
  L 	= 4()bh		Formula for area of 4 triangles.
	= 4()(12)(18)	Replace b with 12 and h with 18.
 	= 432		Simplify.

The surface area needing paint is 432 square meters.  
Compare your answer to the estimate.

Example 3	Surface Area of a Cone
Find the surface area of the cone. Round to the nearest tenth.

S = πr + πr^2	Formula for surface area of a cone
 	= π(6.5)(14.2) + π(6.5)^2	Replace r with 6.5 and  with 14.2.
 	≈ 422.7	Simplify.                                      

The surface area of the cone is about 422.7 square inches.